how to get a smoke domain and flow object to follow a parent that is driven by a rig following follow path bone constraint?
For anyone else who might stumble on this problem, there's nothing different you need to do, but like me you might be thrown off by the viewport showing the smoke sim stuck at frame 1 with the domain not following along with the object, and the smoke sim not updating.

All you need to do is parent all of your smoke objects to any child of the rig that has a path follow constraint (which you've probably already done), and then select the domain and click bake. It will then bake properly. The problem is only that blender tricks you into thinking you've done it wrong for a few hours by giving you the completely wrong result in the viewport unless you bake.

Hope that helps someone.